We present a 3D simulation approach utilising the diffuse interface representation of the phase-field method combined with a heat transfer equation to analyse the thermal conductivity in air-filled aluminium foams with complex cellular structures of different porosity. Algorithmic methods are introduced to create synthetic open-cell foam structures and to compute the thermal conductivity by means of phase-field modelling. A material law for the effective thermal conductivity is derived by determining the appropriate exponent depending on the relative density in the system. The results are compared with the thermal conductivity in massive aluminium and in pure air. (C) 2015 Elsevier Ltd. All rights reserved.